Distributed nested MIMO radar angle and amplitude-phase error joint estimation method under amplitude-phase error condition

Abstract

The invention provides a distributed nested MIMO radar angle and amplitude-phase error joint estimation method under an amplitude-phase error condition, and belongs to the technical field of radar signal processing. The method comprises the following steps: S1, establishing a distributed nested MIMO radar echo signal model, performing matched filtering and vectorization processing on echo signals of a receiving array to obtain a system echo signal model, and determining a covariance matrix R eta eta of the echo signals according to the echo signal model eta (1); step S2, based on steering matrix reconstruction, splitting, selecting and rearranging a covariance matrix R eta eta, constructing a three-order tensor model, and obtaining a preliminary estimation value through decomposition by adopting a COMFAC algorithm; and S3, substituting the initial estimation value obtained by decomposition into a JAAGE algorithm, executing amplitude and phase error estimation by using a Lagrange multiplier, and obtaining an angle pairing estimation result according to the estimated amplitude and phase error.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, and particularly relates to a method for joint estimation of angle and amplitude-phase error of distributed nested MIMO radar under amplitude-phase error conditions. Background Technology

[0002] From a signal processing perspective, the main functions of radar include detection, estimation, tracking, imaging, and identification. Radar direction finding is a crucial component of parameter estimation and one of the core technologies of radar.

[0003] In recent years, MIMO radar based on distributed sub-platforms has made significant progress. Among them, sparse array MIMO radar has advantages such as suppressing mutual coupling, reducing noise coherence, and improving virtual aperture. However, due to non-ideal conditions, the signal will generate amplitude and phase errors during propagation, which will lead to a significant deterioration in target direction finding performance.

[0004] Current joint estimation algorithms for angle and amplitude / phase errors still have many problems. First, some algorithms have limitations and can only be applied to amplitude / phase error correction for monostatic MIMO radars. Second, the angle estimation accuracy of traditional tensor-based algorithms such as the JAAGE algorithm, subspace-based algorithms such as the ESPRIT-like algorithm, and the SCOM algorithm proposed in recent years needs to be improved. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a joint estimation scheme for angle and amplitude / phase error of distributed nested MIMO radar under amplitude / phase error conditions.

[0006] The first aspect of this invention proposes a method for joint estimation of angle and amplitude / phase error in distributed nested MIMO radar under amplitude and phase error conditions, the method comprising:

[0007] Step S1: Establish a distributed nested MIMO radar echo signal model. Perform matched filtering and vectorization processing on the echo signal of the receiving array to obtain the system echo signal model. Based on the echo signal model η (l) Determine the covariance matrix R of the echo signal ηη ;

[0008] Step S2: Based on the guidance matrix reconstruction, reconstruct the covariance matrix R. ηη The process involves splitting, selecting, and rearranging the components, constructing a third-order tensor model, and using the COMFAC algorithm to obtain preliminary estimates through decomposition.

[0009] Step S3: Substitute the preliminary estimated value obtained from the decomposition into the JAAGE algorithm, perform amplitude and phase error estimation using Lagrange multipliers, and obtain the paired estimation result of the angle based on the estimated amplitude and phase error.

[0010] In step S1, the distributed nested MIMO radar consists of m sub-transmitter arrays and n sub-receiver arrays, each sub-array being a nested array, and each transmit sub-array containing M... c N calibration array elements, each receiver subarray containing N c Each calibration array element.

[0011] In step S1, the element positions of both the transmitting and receiving subarrays satisfy the following:

[0012] S t =d{1,2,...,M 11 M 11 +1,...,M 12 (M 11 +1)}

[0013] S t =d{1,2,...,M 11 M 11 +1,...,M 12 (M 11 +1)}

[0014] Where d represents the element spacing; A ri (θ i )=[α ri (θ i1 ),α ri (θ i2 ),…,α ri (θ iK )]、 Let represent the steering matrix of the i-th sub-receive array and the steering matrix of the i-th sub-transmit array, respectively, where:

[0015]

[0016] Let be the steering vectors of the i-th sub-receiver array and the i-th sub-transmitter array about the K-th target, respectively; Let l represent the l-th snapshot signal received by the i-th sub-receiver matrix, where l = 1, 2, ..., L; then, when amplitude and phase errors exist, the received signal matrix can be represented as:

[0017]

[0018]

[0019] The received echo signal is:

[0020]

[0021] but in, Γ represents the signal vector. r =[Γ r1 Γ r2 ... Γ rn ] T For the amplitude and phase error of the receiving array, Γ t =[Γ t1 Γ t2 ... Γ tn ] T Let be the amplitude and phase error of the transmitting array, and:

[0022]

[0023] in, This is the noise matrix received by the i-th sub-receiver matrix.

[0024] In step S1, the received signal is vectorized:

[0025]

[0026] in,

[0027] By combining the matrices corresponding to all the sub-receiver arrays, we obtain:

[0028]

[0029] in, This represents the combination of data vectors received by the i-th sub-receiver array;

[0030] The covariance matrix of the received signal is:

[0031]

[0032] In step S2, for a dual-transmit, dual-receive distributed nested MIMO radar, m = n = 2, and:

[0033]

[0034] The covariance matrix contains four submatrices, each of size (M1N1+M2N1)×(M1N1+M2N1), and N c =M c =2,M 11 =N 11 =3,M 12 =N 12 =4, R η1η1 Decompose it into 14×14 matrices of size 7×7, using This indicates that the position after decomposition is (n) x ,n y A matrix of n, where n x n y ∈[1,7];

[0035] Will After vectorization, we get: Among them, A c express The corresponding guidance matrix; and:

[0036]

[0037] in, It contains mutual information.

[0038] In step S2, based on the steering matrices of the transmit and receive subarrays, using... and Representing the receiving submatrix A respectively r1 The nth x row and nth x If it is done, then Represented as:

[0039]

[0040] Where, when N c =M c =2,M 11 =N 11 =3,M 12 =N 12 =4, It is divided into 196 blocks, each of which is a 7×7 square matrix; after selecting consecutive virtual matrix elements, the newly constructed guiding matrix is ​​represented as:

[0041]

[0042] in, The amplitude and phase error of the virtual receiver subarray corresponding to the new steering matrix; This is the steering matrix corresponding to the virtual receiver subarray.

[0043] In step S2, After all 196 square arrays were selected and reconstructed, they were arranged according to their original positions. The positions in the array are rearranged, and a third-order tensor is constructed. in:

[0044]

[0045] in, Represents tensor operations; for tensor χ c The COMFAC algorithm is used for decomposition to obtain preliminary estimates.

[0046] In step S3, the complete virtual array is divided into two parts, each containing all virtual calibration elements. The JAAGE algorithm is selected to estimate the smoothed subarrays, and the average of the estimation results is taken to obtain the DOA and amplitude / phase error estimates of sub-receiver array 1. Using the same method, the DOA and amplitude and phase error estimates of sub-receiver array 2 are obtained.

[0047] In step S3, for DOD, the covariance matrix R is taken. ηη Four 49×49 square matrices are arranged on the main diagonal. Each of these matrices is divided into 7×7 smaller blocks. Then, consecutive virtual array elements are selected to construct a third-order tensor. The COMFAC algorithm is used for decomposition, and the obtained A' is used... t1 (φ1), A' t1 (φ1)*R s The estimated values ​​were calculated using the JAAGE algorithm to obtain the DOD and amplitude-phase error estimates of sub-transmitter array 1. Similarly, the operation was performed on the other three arrays to obtain the DOD and amplitude-phase error estimates of sub-transmitter array 2.

[0048] A second aspect of this invention proposes a distributed nested MIMO radar angle and amplitude-phase error joint estimation system under amplitude-phase error conditions, the system comprising a processing unit configured to:

[0049] A distributed nested MIMO radar echo signal model is established. Matched filtering and vectorization are performed on the echo signal from the receiving array to obtain the system echo signal model. Based on the echo signal model η... (l) Determine the covariance matrix R of the echo signal ηη ;

[0050] Based on the reconstruction of the guiding matrix, the covariance matrix R ηη The process involves splitting, selecting, and rearranging the components, constructing a third-order tensor model, and using the COMFAC algorithm to obtain preliminary estimates through decomposition.

[0051] Substitute the preliminary estimates obtained from the decomposition into the JAAGE algorithm, use Lagrange multipliers to perform amplitude and phase error estimation, and obtain the paired angle estimation results based on the estimated amplitude and phase errors.

[0052] This invention first constructs a distributed nested MIMO radar echo signal model and preprocesses the received echo signal data to obtain the covariance matrix of the received signal. Then, based on the distribution characteristics of the nested array amplitude and phase errors and virtual array elements, the covariance matrix is ​​divided, selected, and rearranged. A third-order tensor model is constructed by combining the steering matrix reconstruction method. Finally, based on the traditional angle estimation method, the joint estimation of the target angle and amplitude and phase errors is achieved. Attached Figure Description

[0053] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0054] Figure 1 This is a schematic diagram of a distributed nested MIMO radar according to an embodiment of the present invention.

[0055] Figure 2 This is a flowchart illustrating the joint estimation of angle and amplitude / phase error in a distributed nested MIMO radar according to an embodiment of the present invention.

[0056] Figure 3 This is a schematic diagram of the distribution of virtual array elements according to an embodiment of the present invention.

[0057] Figure 4 This is a schematic diagram showing the estimation of DOD1 and DOA1 under the uncorrected condition.

[0058] Figure 5 This is a schematic diagram showing the estimation of DOD2 and DOA2 under the uncorrected condition.

[0059] Figure 6 This is a schematic diagram illustrating the estimation of DOD1 and DOA1 under the algorithm of the present invention.

[0060] Figure 7 This is a schematic diagram illustrating the estimation of DOD2 and DOA2 under the algorithm of the present invention.

[0061] Figure 8 This is a schematic diagram of the amplitude error estimation using the SCOM algorithm.

[0062] Figure 9 This is a schematic diagram of amplitude error estimation under the algorithm of the present invention.

[0063] Figure 10 This is a schematic diagram of phase error estimation using the SCOM algorithm.

[0064] Figure 11 This is a schematic diagram of phase error estimation according to the algorithm of the present invention.

[0065] Figure 12 This is a schematic diagram showing the change in angular RMSE performance with signal-to-noise ratio.

[0066] Figure 13 This is a schematic diagram showing how angular RMSE performance changes with the number of snapshots. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] Definitions of abbreviations and key terms:

[0069] MIMO radar: Multi-Input and Multi-Output radar, mainly refers to a new type of radar system.

[0070] JAAGE: Joint Scheme for Angle and Array Gain-phase Error Estimation, an algorithm for estimating the joint angle and array gain phase error using a three-dimensional tensor structure.

[0071] SCOM: Sparse continuous multiplication, a general DOA estimation algorithm that can be easily applied to coprime arrays and other mainstream DOA estimation techniques.

[0072] COMFAC: Complex Parallel Factor, a tensor decomposition algorithm.

[0073] DOA: Direction of Arrival, the angle of arrival of the target relative to the normal of the receiving array.

[0074] DOD: Direction of Departure, the departure angle of the target relative to the normal of the emission array.

[0075] First Embodiment

[0076] This invention provides a joint estimation scheme for angle and amplitude / phase errors based on tensor decomposition, using a distributed nested MIMO radar as a model. First, a distributed nested MIMO radar echo signal model is constructed, and the received echo signal data is preprocessed to obtain the covariance matrix of the received signal. Then, based on the distribution characteristics of the nested array amplitude / phase errors and virtual array elements, the covariance matrix is ​​divided, selected, and rearranged. A third-order tensor model is constructed using a steering matrix reconstruction method. Finally, based on traditional angle estimation methods, the joint estimation of target angle and amplitude / phase errors is achieved.

[0077] The echo signal model diagram of the distributed nested MIMO radar system to which this invention applies is shown below. Figure 1 As shown; the flowchart of the joint estimation algorithm for angle and amplitude / phase error based on tensor decomposition is as follows: Figure 2 As shown. This invention mainly includes the following steps:

[0078] Step 1: Establish a distributed nested MIMO radar echo signal model. Perform matched filtering and vectorization processing on the echo signal of the receiving array to obtain the system echo signal model. Then, based on the echo signal model η... (l) The covariance matrix R of the echo signal ηη .

[0079] Step 2: Combining the idea of ​​guiding matrix reconstruction, refactor the covariance matrix R. ηη The model is split, selected, and rearranged, and a third-order tensor model is constructed. The COMFAC algorithm is used to decompose the model and obtain preliminary estimates.

[0080] Step 3: Substitute the estimated values ​​obtained from the decomposition into the JAAGE algorithm, use Lagrange multipliers to estimate the amplitude and phase errors, and finally automatically obtain the paired angle estimates based on the estimated amplitude and phase errors.

[0081] Part 1: Model Building

[0082] The distributed nested MIMO radar employed consists of m sub-transmitter arrays and n sub-receiver arrays, where each sub-array is a nested array. Each transmitter sub-array contains M... c N calibration array elements, each receiver subarray containing N c One calibration array element.

[0083] The element positions of both the transmitting and receiving subarrays satisfy the following:

[0084] S t =d{1,2,...,M 11 M 11 +1,...,M 12 (M 11 +1)}

[0085] St =d{1,2,...,M 11 M 11 +1,...,M 12 (M 11 +1)}

[0086] Where d represents the spacing between array elements.

[0087] Use A ri (θ i )=[α ri (θ i1 ),α ri (θ i2 ),…,α ri (θ iK )]and Let represent the steering matrix of the i-th sub-receiving array and the steering matrix of the i-th sub-transmitting array, respectively.

[0088] in

[0089]

[0090] These are the steering vectors of the i-th sub-receiver array and the i-th sub-transmitter array with respect to the K-th target, respectively.

[0091] use Let l represent the l-th snapshot signal received by the i-th sub-receiver matrix, where l = 1, 2, ..., L; then, when amplitude and phase errors exist, the received signal matrix can be represented as:

[0092]

[0093] The received echo signal is:

[0094]

[0095] Therefore, there is

[0096] in Γ represents the signal vector. r =[Γ r1 Γ r2 ... Γ rn ] T For the amplitude and phase error of the receiving array, Γ t =[Γ t1 Γ t2 ... Γ tn ] T The amplitude and phase error of the transmitting array,

[0097] This is the noise matrix received by the i-th sub-receiver matrix.

[0098] Vectorization of the received signal yields:

[0099]

[0100] in,

[0101] By combining the matrices corresponding to all the sub-receiver arrays, we can obtain:

[0102]

[0103] in, This represents the combination of data vectors received by the i-th sub-receiver array.

[0104] The covariance matrix of the received signal is:

[0105]

[0106] Part Two: Joint Estimation Algorithm for DOD, DOA, and Amplitude / Phase Errors

[0107] The data model is set as a dual-transmitter dual-receiver distributed nested MIMO radar, i.e., m=n=2.

[0108]

[0109] It can be seen that the covariance matrix contains four submatrices, each of which is a square matrix of size (M1N1+M2N1)×(M1N1+M2N1). For ease of analysis, let M be taken here. c =M c =2,M 11 =N 11 =3,M 12 =N 12 =4. With For example, it can be decomposed into 14×14 matrices of size 7×7, using... This indicates that the position after decomposition is (n) x ,n y A matrix of n, where n x n y ∈[1,7].

[0110] Will Vectorization yields: Where A c express The corresponding guidance matrix.

[0111]

[0112] in It contains mutual information.

[0113] Based on the steering matrices of the transmit and receive subarrays, using and Representing the receiving submatrix A respectively r1 The nth x row and nth x If it is done, then It can be represented as:

[0114]

[0115] When N c =M c =2,M 11 =N 11 =3,M 12 =N 12 =4, It can be divided into 196 blocks, each of which is a 7×7 square matrix, and the positions of its elements are distributed as follows: Figure 3 As shown in the figure. The parts marked in green and red can be represented as continuous virtual array elements, and the green part is the calibration virtual array element.

[0116] It can be seen that the value range of continuous array elements is [-15, 15], and the value range of calibration virtual array elements is [-1, 1].

[0117] After selecting consecutive virtual array elements, the newly constructed steering matrix is ​​represented as:

[0118]

[0119] in The amplitude and phase error of the virtual receiver subarray corresponding to the new steering matrix; This is the steering matrix corresponding to the virtual receiver subarray.

[0120] Will After all 196 square matrices have been selected and reconstructed as described above, they can be arranged according to their original positions. The positions in the array are rearranged, and a third-order tensor is constructed.

[0121]

[0122] in, Represents tensor operations.

[0123] For tensor χ c The estimated value can be obtained by decomposing the material using the COMFAC algorithm.

[0124] Since the filtered virtual array elements are continuous, and the calibration element is located at the center of the array, a smoothing operation is required when estimating the angle and amplitude / phase errors. This involves dividing the complete virtual array into two parts (each containing all virtual calibration elements). Then, a traditional algorithm (such as the JAAGE algorithm) can be used to estimate the angle and amplitude / phase errors of these two smoothed subarrays, and the results are averaged to improve performance. Using this method, the estimated DOA (DOA1) and amplitude / phase errors of sub-receiver array 1 can be obtained. The same method can be used to obtain the DOA (denoted as DOA2) and amplitude and phase error estimates of sub-receiver array 2.

[0125] For DOD, the covariance matrix R is taken. ηη The four 49×49 square matrices on the main diagonal are each divided into 7×7 smaller blocks, and then each is further divided according to... Figure 2 The location distribution map selects consecutive virtual array elements. Taking the first square array in the upper left corner of the four square arrays as an example, a third-order tensor is constructed. After decomposing using the COMFAC algorithm, the obtained The estimated values ​​can be used to calculate the DOD (denoted as DOD1) and amplitude and phase error estimates of sub-transmitter array 1 using the JAAGE algorithm. Similarly, by operating on the other three arrays, the DOD (denoted as DOD2) and amplitude and phase error estimates of sub-transmitter array 2 can be obtained.

[0126] Second Embodiment

[0127] The simulation experiment uses a dual-transmitter, dual-receiver nested MIMO radar, and assumes that the amplitude and phase error distribution satisfies:

[0128]

[0129]

[0130] Where, σ ρti , σ ρri , σ φti , σ φri ρ ti,m , ρ ri,n , φ ti,m , φ ri,n The error coefficient, amplitude error coefficient σ ρ =σ ρti =σ ρri Phase error coefficient σ φ =σ φti =σ φri ξ m ξn , ζ m , ζ n Let be an independent and identically distributed random variable that follows a uniform distribution in the range [-0.5, 0.5].

[0131] The angle RMSE (root mean square error) is defined as:

[0132]

[0133] in, This indicates the number of Monte Carlo experiments performed. and for and θ jk The estimated value is given by K, which represents the number of targets to be detected. Different targets and the number of snapshots are set for different experiments.

[0134] Regarding the joint estimation results of DOD, DOA, and amplitude and phase errors, we assume there are K=5 far-field incoherent targets, and set the DOD and DOA of these five targets as follows:

[0135]

[0136] θ1=(-5°,10°,30°,40°,50°), θ2=(-15°,10°,35°,55°,65°)

[0137] And set the amplitude error coefficient σ ρ =0.2, phase error coefficient σ φ =30°, SNR=15dB, L=500. The angle estimation results of the 2D-UESPRIT (2Dimension-Unitary ESPRIT) algorithm without amplitude and phase error correction and the algorithm in this paper are as follows: Figure 4-7 As shown.

[0138] Figure 4-7 The single-angle RMSE values ​​are 9.303, 17.939, 0.113, and 0.0902, respectively. Furthermore, as can be seen from the figure, under this algorithm, the target's DOD relative to the transmitting array and DOA relative to the receiving array can be accurately and effectively identified. The simulation results intuitively demonstrate that the algorithm presented in this paper has superior angle estimation performance under amplitude and phase error conditions.

[0139] Figure 8-11 The amplitude and phase error estimation results for receiver array 1 and transmitter array 1 obtained by the SCOM algorithm and the algorithm in this paper are respectively. Figure 8-11As shown, both algorithms can accurately estimate the amplitude and phase errors, with corresponding single array calibration RMSEs of 0.0039 and 0.0017, respectively. In comparison, the algorithm presented in this paper has better amplitude and phase error estimation performance.

[0140] Regarding the algorithm performance comparison analysis, an amplitude error coefficient σ is set for comparing algorithm performance under different signal-to-noise ratios. ρ =0.2, phase error coefficient σ φ =30°, L=500, within the signal-to-noise ratio (SNR) range of [-5, 0, 5, 10, 15, 20], the RMSE for angle estimation using the JAAGE algorithm, SCOM algorithm, ESPRIT-like algorithm, and the algorithm of this invention are calculated respectively. Experimental results are as follows: Figure 12 As shown. From Figure 12 As can be seen, under low signal-to-noise ratio (SNR < 0dB) conditions, the error of the SCOM algorithm increases significantly, and the direction-finding performance decreases markedly. This phenomenon is caused by the SCOM algorithm failing to estimate angles under low SNR conditions. Under SNR > 0dB conditions, the performance of the four algorithms, from best to worst, is as follows: the algorithm of this invention, the JAAGE algorithm, the SCOM algorithm, and the ESPRIT-like algorithm. Among them, the JAAGE algorithm, which uses a three-dimensional structure, performs slightly better than the ESPRIT-like algorithm, while the algorithm of this invention not only utilizes the three-dimensional structure of the tensor but also effectively utilizes the virtual aperture of the receiving array, thus achieving the best performance.

[0141] To compare algorithm performance under different snapshot counts, an amplitude error coefficient σ was set. ρ =0.2, phase error coefficient σ φ =30°, SNR=15dB, calculate the RMSE of angle estimation using the JAAGE algorithm, SCOM algorithm, ESPRIT-like algorithm, and the algorithm of this invention when the number of snapshots L=[200, 300, 400, 500, 600, 700, 800, 900, 1000]. Experimental results are as follows: Figure 13 As shown. From Figure 13 As can be seen, the direction finding error of all four algorithms decreases as the signal-to-noise ratio increases. Among them, the SCOM algorithm performs slightly better than the ESPRIT-like algorithm, and the algorithm of this invention still has the best performance compared to the other three algorithms.

[0142] In summary, this invention, starting from improving the accuracy of system angle estimation under amplitude and phase error conditions, designs a direction-finding algorithm for distributed nested MIMO radar systems. Compared to other algorithms, this algorithm applies the idea of ​​guidance matrix reconstruction, which not only effectively utilizes the virtual aperture of the nested array but also leverages the high-dimensionality advantage of tensors. Furthermore, it allows for the effective use of information in the covariance matrix, thus exhibiting superior performance in DOA estimation.

[0143] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above embodiments only illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims

1. A method for joint estimation of angle and amplitude / phase error in distributed nested MIMO radar under amplitude and phase error conditions, characterized in that, The method includes: Step S1: Establish a distributed nested MIMO radar echo signal model. Perform matched filtering and vectorization processing on the echo signal of the receiving array to obtain the system echo signal model. Based on the echo signal model η (l) Determine the covariance matrix R of the echo signal ηη ; Step S2: Based on the guidance matrix reconstruction, reconstruct the covariance matrix R. ηη The process involves splitting, selecting, and rearranging the components, constructing a third-order tensor model, and using the COMFAC algorithm to obtain preliminary estimates through decomposition. Step S3: Substitute the preliminary estimated value obtained from the decomposition into the JAAGE algorithm, perform amplitude and phase error estimation using Lagrange multipliers, and obtain the paired estimation result of the angle based on the estimated amplitude and phase error.

2. The method for joint estimation of angle and amplitude / phase error of distributed nested MIMO radar under amplitude / phase error conditions according to claim 1, characterized in that, In step S1, the distributed nested MIMO radar consists of m sub-transmitter arrays and n sub-receiver arrays, each sub-array being a nested array, and each transmit sub-array containing M... c N calibration array elements, each receiver subarray containing N c Each calibration array element.

3. The method for joint estimation of angle and amplitude / phase error of distributed nested MIMO radar under amplitude / phase error conditions according to claim 2, characterized in that, In step S1, the element positions of both the transmitting and receiving subarrays satisfy the following: S t =d{1,2,...,M 11 ,M 11 +1,...,M 12 (M 11 +1)} S t =d{1,2,...,M 11 ,M 11 +1,...,M 12 (M 11 +1)} Where d represents the element spacing; A ri (θ i )=[α ri (θ i1 ),α ri (θ i2 ),…,α ri (θ iK )]、 Let represent the steering matrix of the i-th sub-receive array and the steering matrix of the i-th sub-transmit array, respectively, where: Let be the steering vectors of the i-th sub-receiver array and the i-th sub-transmitter array about the K-th target, respectively; Let l represent the l-th snapshot signal received by the i-th sub-receiver matrix, where l = 1, 2, ..., L; then, when amplitude and phase errors exist, the received signal matrix can be represented as: The received echo signal is: but in, Γ represents the signal vector. r =[Γ r1 Γ r2 ...Γ rn ] T For the amplitude and phase error of the receiving array, Γ t =[Γ t1 Γ t2 ...Γ tn ] T Let be the amplitude and phase error of the transmitting array, and: in, This is the noise matrix received by the i-th sub-receiver matrix.

4. The method for joint estimation of angle and amplitude / phase error of distributed nested MIMO radar under amplitude and phase error conditions according to claim 3, characterized in that, In step S1, the received signal is vectorized: in, By combining the matrices corresponding to all the sub-receiver arrays, we obtain: in, This represents the combination of data vectors received by the i-th sub-receiver array; The covariance matrix of the received signal is:

5. The method for joint estimation of angle and amplitude / phase error of distributed nested MIMO radar under amplitude / phase error conditions according to claim 4, characterized in that, In step S2, for a dual-transmit, dual-receive distributed nested MIMO radar, m = n = 2, and: The covariance matrix contains four submatrices, each of size (M1N1+M2N1)×(M1N1+M2N1), and N c =M c =2,M 11 =N 11 =3,M 12 =N 12 =4, will Decompose it into 14×14 matrices of size 7×7, using This indicates that the position after decomposition is (n) x ,n y A matrix of n, where n x n y ∈[1,7]; Will After vectorization, we get: Among them, A c express The corresponding guidance matrix; and: in, It contains mutual information.

6. The method for joint estimation of angle and amplitude / phase error of distributed nested MIMO radar under amplitude and phase error conditions according to claim 5, characterized in that, In step S2, based on the steering matrices of the transmit and receive subarrays, using... and Representing the receiving submatrix A respectively r1 The nth x row and nth x If it is done, then Represented as: Where, when N c =M c =2,M 11 =N 11 =3,M 12 =N 12 =4, It is divided into 196 blocks, each of which is a 7×7 square matrix; after selecting consecutive virtual matrix elements, the newly constructed guiding matrix is ​​represented as: in, The amplitude and phase error of the virtual receiver subarray corresponding to the new steering matrix; This is the steering matrix corresponding to the virtual receiver subarray.

7. The method for joint estimation of angle and amplitude / phase error of distributed nested MIMO radar under amplitude / phase error conditions according to claim 6, characterized in that, In step S2, After all 196 square arrays were selected and reconstructed, they were arranged according to their original positions. The positions in the array are rearranged, and a third-order tensor is constructed. in: in, Represents tensor operations; for tensor χ c The COMFAC algorithm is used for decomposition to obtain preliminary estimates.

8. The method for joint estimation of angle and amplitude / phase error of distributed nested MIMO radar under amplitude / phase error conditions according to claim 7, characterized in that, In step S3, the complete virtual array is divided into two parts, each containing all virtual calibration elements. The JAAGE algorithm is selected to estimate the smoothed subarrays, and the average of the estimation results is taken to obtain the DOA and amplitude / phase error estimates of sub-receiver array 1. Using the same method, the DOA and amplitude and phase error estimates of sub-receiver array 2 are obtained.

9. The method for joint estimation of angle and amplitude / phase error of distributed nested MIMO radar under amplitude and phase error conditions according to claim 8, characterized in that, In step S3, for DOD, the covariance matrix R is taken. ηη Four 49×49 square matrices are arranged on the main diagonal. Each of these matrices is divided into 7×7 smaller blocks. Then, consecutive virtual array elements are selected to construct a third-order tensor. The COMFAC algorithm is used for decomposition, and the obtained A' is used... t1 (φ1), A' t1 (φ1) * R s The estimated values ​​were calculated using the JAAGE algorithm to obtain the DOD and amplitude-phase error estimates of sub-transmitter array 1. Similarly, the operation was performed on the other three arrays to obtain the DOD and amplitude-phase error estimates of sub-transmitter array 2.

10. A distributed nested MIMO radar angle and amplitude / phase error joint estimation system under amplitude and phase error conditions, characterized in that, The system includes a processing unit, which is configured to: A distributed nested MIMO radar echo signal model is established. Matched filtering and vectorization are performed on the echo signal from the receiving array to obtain the system echo signal model. Based on the echo signal model η... (l) Determine the covariance matrix R of the echo signal ηη ; Based on the reconstruction of the guiding matrix, the covariance matrix R ηη The process involves splitting, selecting, and rearranging the components, constructing a third-order tensor model, and using the COMFAC algorithm to obtain preliminary estimates through decomposition. Substitute the preliminary estimates obtained from the decomposition into the JAAGE algorithm, use Lagrange multipliers to perform amplitude and phase error estimation, and obtain the paired angle estimation results based on the estimated amplitude and phase errors.

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